The space of Bridgeland stability conditions \(\operatorname{Stab}(\mathcal {C})\)  on \(\mathcal {C}=D^b(\operatorname{Coh}_c K_{{P}^2})\) 
was studied in [1]}, [2]}. After fixing the \({C}^\times \)  action
such that skyscraper sheaves have central charge \(Z_{[0,0,1]}=-1\) , the central charge
can be parametrized by the two complex coefficients \((T,T_D)\)  in (REF ),
\(Z(\gamma ) = - r T_D + d T -\textnormal {ch}_2\) 
